Trump was asked by a reporter while holding a Cabinet meeting at the White House whether he deserved the honor, to which the President replied with a large smile: "Everyone thinks so, but I would never say it."

Trump instead said he's focused on getting an agreement with North Korea "finished."

"The prize I want is victory for the world. Not for even here -- I want victory for the world 'cause that's what we're talking about. So that's the only prize I want," Trump said in the Cabinet room.

The Nobel Peace Prize is one of six awards given yearly by the Nobel Committee. Nobel prizes are usually announced in October but awarded annually on December 10, the anniversary of death of Alfred Nobel, who gives his name to the awards.

If Trump were to win the award, he'd be the fifth American president bestowed with the honor. Presidents Theodore Roosevelt, Woodrow Wilson, Jimmy Carter and Barack Obama are all Nobel winners. During a recent campaign-style rally in Michigan, the crowd broke out into a chant of "Nobel, Nobel" while Trump was discussing his efforts in North Korea. Clearly enjoying the response, the President smiled and said, "Thank you, that is very nice."

In late April, South Korean President Moon Jae-in said that Trump would be a worthy winner of the Nobel Peace Prize, following his own summit with Kim Jong Un.

"President Trump should win the Nobel Peace Prize. The only thing we need is peace," Moon said, according to the Blue House, the South Korean presidential office.

On Wednesday, Trump sounded optimistic about his upcoming meeting with Kim.

"A lot of things can happen," Trump said regarding the meeting. "A lot of good things can happen. A lot of bad things can happen. I believe that we have both sides want to negotiate a deal. I think it's going to be a very successful deal. I think we have a really good shot at making it successful."

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